The elemental compositions of planet hosting stars serve as proxies for the primordial compositions of the protoplanetary disks within which the planets form. The temperature profile of the disk governs the condensation fronts of various compounds, and although these chemically distinct regions migrate and mix during the disk lifetime, they can still leave an imprint on the compositions of the forming planets. Observable atmospheric compositions of hot Jupiters when compared against their host stars could potentially constrain their formation and migration processes. We compared the measured planetary and stellar abundances of carbon and oxygen for ten systems with hot Jupiters. If the planets formed by core accretion with significant planetesimal accretion and migrated through the disk, the hot Jupiter atmospheres should be substantially super-stellar in O/H and sub-stellar in C/O. On the contrary, however, we find that currently reported abundances of hot Jupiters have generally super-stellar C/O ratios, though present uncertainties on the reported O/H and C/O ratios are too large to reach a firm conclusion. In one case however, HD 209458b, the elevated C/O and depleted O/H of the planet compared to the host star is significant enough to suggest an origin far beyond the ice line, with predominantly gas accretion, and subsequent disk-free migration. Improved measurements from the James Webb Space Telescope will enable more precise measurements for more hot Jupiters and we predict, based on the current marginal trend, that a sizable fraction of hot Jupiters will show enrichment of C/O and lower O/H than their hosts, similar to HD 209458b.

A simplified description of the ideas in this paper is as follows:

Within the water ice line at ~3 AU, the protoplanetary gas has composition close to that of the star.

Outside of the water ice line, H2O locks up a significant proportion of Oxygen in the disk while Carbon is not significantly affected.

C/O ratios in giant planets elevated above the stellar abundances indicates formation beyond the water ice line without significant accretion of material found closer in.

Thus, Hot Jupiters with elevated C/O were not interior to the water ice line while substantial volatiles were present (up to several Myr in system age), so they must have formed beyond the water-ice line and migrated in considerably later.

While current measurements are found to be largely too imprecise to be useful, as stated in the abstract the composition of HD 209458 b is consistent with formation beyond the ice line with little accretion of O-rich volatiles on its way in. This supports a dynamical migration scenario for HD 209458 b, rather than migration via the disk.

With improvements to abundance measurement data coming in the near future, I expect it will be possible to revisit this with more stringency in some years. It will be interesting to observe the frequencies of in-disk and dynamical migration of Hot Jupiters, in particular if their is any relationship with the presence of additional planets.